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Appendix E
Game theory
One way of looking at collaboration is to take a game theory approach. Game theory
is a way of looking at problems in terms of the ‘payoff’ given to the various ‘players’
based on their behaviour.
An example of this is the Prisoner’s Dilemma. This is a two player game, where
both players have been caught by the police for a serious crime. The police have
enough evidence to convict both on minor charges, but not enough to convict them
of the serious offense. Each is questioned individually. If both remain silent, they
both receive minor prison sentences. If one informs on the other, the informer goes
free and the other receives a long prison sentence. If both inform then they both
receive a medium length sentence. This can be expressed as a payoff matrix (see
Table E.1), where the two values are the respective payoffs for the two players.
Although the optimum decision for the two prisoners together would be to collaborate, this behaviour has a considerably greater risk associated with it and is not
the best possible outcome for each player individually. If each of the options are
examined separately, defection (informing on the other prisoner) will always be the
safer option — if they also inform, the sentence is reduced from 1 year to 3 months.
If they do not, the sentence is reduced from 1 month to nothing. However, as both
players know this it is most likely that both will defect and receive the second worst
option instead of collaborating and receiving the second best.
Many situations can be modelled as games, with varying numbers of players
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